x is an integer.
The Lowest Common Multiple (LCM) of x and 12 is 120
The Highest Common Factor (HCF) of x and 12 is 4
Work out the value of x
Answers
Since 120 = 12 • 10 and LCM(x, 12) = 120, these suggest x is some multiple of 10.
HCF(x, 12) = 4 tells us that x is a multiple of 4.
If x is a both a multiple of 4 and 10, then the smallest x that fits both conditions is 4 • 10 = 40. (-40 also satisfies the criteria.)
The value of x for which the LCM and HCF of x and 12 are 120 and 4 respectively is 40.
What do we mean by Lowest Common Multiple (LCM) and Highest Common Factor (HCF)?
The Lowest Common Multiple (LCM) of the numbers is the smallest common multiple of the given numbers.
The Highest Common Factor (HCF) of the numbers is the greatest factor of the given numbers.
In the case of two numbers, the product of LCM and HCF is equal to the product of the numbers.
How do we solve the given question?We are given two numbers, x and 12.
Their LCM and HCF are 120 and 4 respectively.
We are asked to find the number x.
For two numbers, we know that the product of two numbers is equal to the product of their HCF and LCM.
∴ x*12 = 120*4
or, 12x = 480
or, x = 480/12
or, x = 40.
∴ The value of x for which the LCM and HCF of x and 12 are 120 and 4 respectively is 40.
Learn more about HCF and LCM at
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Related Questions
Math Practices and Problem Sol
17. Number Sense Using three different
numerators, write an equation in which
three fractions, when added, have a
sum of 1.
Answers
Answer:
First choose a common denominator, here i picked 11 then we think of 3 diffrent numbers so that their sum is 11 such as 2+4+5=11 so a possible equasion would be
Step-by-step explanation:
What are the solutions of 12 - x2 =0?
O x=2/3 and x = -2/3
O x= 3, and x = -373
O x= 4,3 and x = -4/3
O x=6 and x = -6
Answers
Two consecutive positive integers have a product of 156. Find the integers.
The integers are ___
Answers
So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!
So let us assume the unknown positive integers as a and (a + 1).
★ Product of both integers :-
a (a + 1) = 156 [Equation formed]★ Solving the equation :-
[tex]: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}[/tex]
Therefore,
First positive integer is 12★ Second positive integer :-
2nd positive integer = a + 1 2nd positive integer = 12 + 1 2nd positive integer = 13dont mind my answers thanks for helping me out have a good day
Answers
Answer:
ACD and DCB are supplementary and others are correctly chosen ...
Help!! Khan academy geomtry practice
Answers
Answer:
33.51 units³
Step-by-step explanation:
Volume of a sphere is given by the formula :
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
Because we have the radius we can plug it into the equation to give us :
V = (4/3)×π×(2)³
V = 4/3×8π
V ≈ 33.51
Units will be units³ since no measurement is given but it to the power of 3 since it is volume.
The table shows the average bill totals for given numbers of diners at Simone’s restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?
Persons Bill Amount
1 ------------$40
2 $80
7 -------------$280
9 $360
11 $440
A.(12, 460
B.(20, 800)
C.(24, 1,020
D.(27, 1,080)
E.(28, 1,110)
HELPP
Answers
Answer:
(B) and (D)
Step-by-step explanation:
it's B and D because they are the only two points with constant rate
I’ll give you brainliest for the first person with an answer
Answers
Answer:
1296mm^2
Step-by-step explanation:
Surface Area of the Rectangular Prism to the left on top of the box:
Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving 162mm^2
Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving 162mm^2
So, the total surface area of the rectangular prism to the left on top, is 324mm^2
Surface Area of the Triangular Prism:
Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get 108mm^2.
Area of the rectangle: lw, so 15mm * 9mm = 135mm^2
So, the total surface area of the triangular prism is 243mm^2
Surface Area of the Rectangular Prism at the bottom:
Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, 378mm^2
Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, 162mm^2
Area of the rectangle at the very bottom = lw, 21mm * 9mm = 189mm^2
So, the total surface area of the rectangular prism at the bottom is 729mm^2
Add all the total surface areas of each shape to get the total surface area of the figure:
324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2
The surface area of the figure above is 1296mm^2
A company makes concrete bricks that are shaped like rectangular prisms. Each brick is 5inches long, 4inches wide, and 2inches tall. How much concrete will they need to make 1600 bricks?
Answers
Answer:
The answer would be 64,000.
Step-by-step explanation:
To find the area of one concrete block you will multiple length x width x height. Using the measurements provided, one block will equal 40. You will then multiple this by 1,600 to equal 64,000.
MAn article is
bought and sold at a profit of one fourth of selling
price. Find the profit percent.
Answers
Answer:
25% profit
Step-by-step explanation:
Statement
An article is bought and sold at a profit of one fourth of selling price.
⇒ Buying price = x
⇒ Selling price = Buying price (1 + 1/4) = 5x/4
Profit %
Selling price - Buying price / Buying price(5x/4 - x) / x(x/4) / x⇒ 1/4⇒ 0.25⇒ 25% profitWhat was one of the main causes of the Great Depression?
a. The overuse of credit
b. The under-utilization of money
c. WWII
d. Excessive government borrowing
Answers
Answer:
B
Step-by-step explanation:
4/9÷1/2 as a fraction (simplest form)
Answers
Answer:
8/9
Step-by-step explanation:
4/9 ÷ 1/2 = dividing by 1/2 is the same as multiplying by its reciprocal 2/1
4/9 × 2/1 = (4×2)/(9×1) multiply numerators (top numbers) and multiply denominators (bottom numbers)
The strength of an electrical current x flowing through the electric circuit shown is expressed as a function of time t and satisfies the following differential equation:
[tex]\displaystyle \large{L \frac{dx}{dt} + Rx = V}[/tex]
Find the strength of the electrical current x after switch S is closed at time t = 0. Assume that L, R and V are positive constants, and also that x = 0 when t = 0. Then, find [tex]\displaystyle \large{ \lim_{t \to \infty} x}[/tex]
Topic: Application of Differential Equation Reviews
Answers
Answer:
The current of the circuit at t = 0 is equal to 0.
If we take the limit as t approaches infinity, the current is equal to ε/R or V/R.
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]
Derivative Rule [Basic Power Rule]:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Slope Fields
Separation of VariablesIntegration
IntegralsIntegration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Method: U-Substitution
Electricity
Ohm's Law: V = IR
V is voltage (in Volts)I is current (in Amps)R is resistance (in Ohms)Circuits
Circuit SymbolsKirchhoff's Laws (Loop and Junction Rule)InductorsStep-by-step explanation:
*Note:
In the given equation, our variable of differentiation is x. I will rewrite this as current I for physics notation purposes.
Step 1: Define
Identify given.
[tex]\displaystyle L \frac{dI}{dt} + RI = V[/tex]
[Assuming switch S is closed] Recall that an inductor is used in a circuit to resist change. After a long period of time, when it hits steady-state equilibrium, we expect to see the inductor act like a wire.
Step 2: Find Current Expression Pt. 1
[Kirchhoff's Law] Rewrite expression:[tex]\displaystyle L \frac{dI}{dt} = V - IR[/tex]Rewrite expression by dividing R on both sides:
[tex]\displaystyle \frac{L}{R} \frac{dI}{dt} = \frac{\mathcal E}{R} - I[/tex]
Step 3: Find Current Expression Pt. 2
Identify variables for u-substitution.
Set u:[tex]\displaystyle u = \frac{\mathcal E}{R} - I[/tex][u] Differentiation [Derivative Rules and Properties]:
[tex]\displaystyle du = - \, dI[/tex]
Step 4: Find Current Expression Pt. 3
[Kirchhoff's Law] Apply U-Substitution:[tex]\displaystyle - \frac{L}{R} \frac{du}{dt} = u[/tex][Kirchhoff's Law] Apply Separation of Variables:
[tex]\displaystyle \frac{1}{u} \, du = -\frac{L}{R} \, dt[/tex]
Recall that our initial condition is when t = 0, denoted as u₀, and we go to whatever position u we are trying to find. Also recall that time t always ranges from t = 0 (time can't be negative) and to whatever t we are trying to find.
[Kirchhoff's Law] Integrate both sides:[tex]\displaystyle \int\limits^u_{u_0} {\frac{1}{u}} \, du = \int\limits^t_0 {- \frac{R}{L}} \, dt[/tex][Kirchhoff's Law] Rewrite [Integration Property]:
[tex]\displaystyle \int\limits^u_{u_0} {\frac{1}{u}} \, du = - \frac{R}{L} \int\limits^t_0 {} \, dt[/tex][1st Integral] Apply Logarithmic Integration:
[tex]\displaystyle \ln | u | \bigg| \limits^u_{u_0} = - \frac{R}{L} \int\limits^t_0 {} \, dt[/tex][2nd Integral] Apply Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \ln | u | \bigg| \limits^u_{u_0} = - \frac{R}{L} t \bigg| \limits^t_0[/tex]Apply Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \ln | \frac{u}{u_0} | = - \frac{R}{L} t[/tex]Apply e to both sides:
[tex]\displaystyle e^{\ln | \frac{u}{u_0} |} = e^{- \frac{R}{L} t}[/tex]Simplify:
[tex]\displaystyle \frac{u}{u_0} = e^{- \frac{R}{L} t}[/tex]Rewrite:
[tex]\displaystyle u = u_0 e^{- \frac{R}{L} t}[/tex]
Recall that our initial condition u₀ (derived from Ohm's Law) contains only the voltage across resistor R, where voltage is supplied by the given battery. This is because the current is stopped once it reaches the inductor in the circuit since it resists change.
Back-Substitute in u and u₀:[tex]\displaystyle \frac{\mathcal E}{R} - I = \frac{\mathcal E}{R} e^{- \frac{R}{L} t}[/tex]Solve for I:
[tex]\displaystyle I = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t}[/tex]
Step 5: Solve
If we are trying to find the strength of the electrical current I at t = 0, we simply substitute t = 0 into our current function:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\I(0) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(0)} \\& = \boxed{\bold{0}}\end{aligned}[/tex]
If we are taking the limit as t approaches infinity of the current function I(t), we are simply just trying to find the current after a long period of time, which then would just be steady-state equilibrium:
[tex]\displaystyle\begin{aligned}I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}t} \\\lim_{t \to \infty} I(t) & = \frac{\mathcal E}{R} - \frac{\mathcal E}{R} e^{- \frac{R}{L}(\infty)} \\& = \boxed{\bold{\frac{\mathcal E}{R}}}\end{aligned}[/tex]
∴ we have found the current I at t = 0 and the current I after a long period of time and proved that an inductor resists current running through it in the beginning and acts like a wire when in electrical equilibrium.
---
Topic: AP Physics C - EMAG
Unit: Induction
Use the regression equation to predict the sales of skin diving and scuba equipment in the year 2008
Answers
Answer:c
Step-by-step explanation:
Find the perimeter of the parallelogram.
Will mark brainlyest!!
Answers
Answer:
58cm
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
16 +16=32
13+13=26
32+26=58
Hope it Helps
Find the surface area of the right triangular prism (above) using its net (below).
Answers
Answer:
The Answer is 96 units squared
Step-by-step explanation:
First, you find the area of all the sides:
Triangle 1: 6
Triangle 2: 6
Rectangle 1: 21
Rectangle 2: 28
Rectangle 3: 35
Then you add all of the numbers together.
6+6+21+28+35 = 96 units squared
I hope this helps :)
What’s The Answer Of This? Please HELP FAST
Answers
Answer:
those are corrisponding angles which means they equal each other making <H and <G both 57 degrees
*URGENT*
If you were at the Market Square and you wanted to get to the Doctor’s Office, according to the map, how would you get there? (Write your answer according to units.)
Answers
Answer: (2,-5) X:2. Y:-5
Move accross 2 units to the right and then 5 units down from 2
What is the equation of a line that passes through the hypotenuse of the right triangle in the graph?
A. 1/5x
B. y=5x
C. y=-5x
D. y=2/5x
Answers
Answer:
y = 5x
Step-by-step explanation:
Hey there!
To start with the hypotenuse of a triangle is the longest side of it
and to get an equation of a line you would use
y = mx + b
where m is the slope
and b is the y-intercept
to get the slope you would do rise over run
rise/run
take 2 points and see how much it rises and runs to the next point
you would then get 5
then we figure out the y-intercept where the line intercepts the y-axis
in this case 0
In conclusion the answer is y = 5x + 0
we can also remove the 0 because it is unnecessary
y = 5x
Help for the brainiest answer quickly please
Answers
Answer:
C
Step-by-step explanation:
use an equation to find the value of k so that the line that passes through (1,3) and (5,k) has a slope of m=2.
Answers
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11[/tex]
A baseball field in the shape of a square is shown. the corners are labeled home plate, first base, second base, and third base. the distance between home plate and first base is 90 feet. a baseball field is in the shape of a square. the distance between each pair of bases along the edge of the square is 90 feet. what is the distance between home plate and second base? startroot 2 endroot feet
Answers
Answer:
90√2 feet
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle with sides 90 feet. The length of the hypotenuse is the distance from home plate to 2nd base. The Pythagorean theorem tells you that distance (c) is ...
c² = a² +b²
c² = (90 ft)² +(90 ft)² = 8100 ft² +8100 ft²
c² = 16200 ft²
c = √16200 ft = 90√2 ft
The distance between home plate and second base is 90√2 feet.
Answer:
A baseball field is in the shape of a square. The distance between each pair of bases along the edge of the square is 90 feet. What is the distance between home plate and second base?
(90) StartRoot 2 EndRoot feet
Step-by-step explanation:
show how to rewrite 1/5 with the denominator of 10
Answers
Answer:
2/10
Step-by-step explanation:
Since the denominator is 10, we must find what the numerator is so that the fraction can be equal to 1/5. Since 10 is twice of 5, we multiply 2 by 2 as well. With that, we get a final answer of 2/10.
Find the missing measurement for x.
Answers
Answer:
EASYYY 90°
Step-by-step explanation:
30 + 60 = 90
180-90=90
also
thats a right angle which is always 90°
ALSO
the angle opposite another angle is always the same measurement.
A radioactive element decays at a rate of 5.25% annually. There are 35 grams of the substance
present. How much of the substance remains after 12 years (Round to the nearest hundredth)?
TEKS A2.5(B)(D)
Answers
Answer:
18.32 gm
Step-by-step explanation:
= 35 ( 1-.0525)^12 = 18.32 gm remain
Find, from first principle the derivative of 1/x^2+1 with respect to x.
Answers
Answer:
d/dx = -2/x^3
Step-by-step explanation:
1/x^2 + 1
We can solve for the derivative using the power rule
d/dx = -2/x^3 + 0
d/dx = -2/x^3
If x = 18, evaluate the following expression:
12 + 3
Answers
30
Explanation
12+18=30
please help me, thank you if you do
Answers
Answer:
Step-by-step explanation:
1. The sequence is not arithmetic.
2. d=-30
A rectangle has vertices at coordinates 0,0 3,0 0,6 what is the area of the rectangle
Answers
Answer:
18
Step-by-step explanation:
Solve 196x2 + 25 = 0 by using square roots.
Answers
f(3) if f(x) = 2x + 5 =
Answers
Answer:
11
Step-by-step explanation: Uh- if X=3 then it would be 2(3) +5. 2x3 is 6, and 6+5 is 11.
Answer:
11
Step-by-step explanation:
2(3) + 5
simplify
6 + 5 = 11
hope this helps